[petsc-users] Mixed matrices MatMatMult

[Matthew Knepley]

On Thu, Mar 26, 2015 at 4:06 PM, Luc Berger-Vergiat <lb2653 at columbia.edu>
wrote:

>  Ok,
> this work is still part of my Schur complement approach using the full
> schur but with a block diagonal A00^-1.
> I implemented the computation of A00^-1 by extracting each diagonal block
> and inverting them individually.
> This works quite well and does not cost some much, especially since I can
> still use threads to accelerate this process (I might send a question about
> this in the future...).
>
> At the moment the most expensive part of the procedure is inverting S (I'm
> using LU at the moment to make sure that everything is implemented
> correctly) and the second most expensive procedure is MatMatMult. I'm doing
> two of these: A10 * A00^-1 and then a right multiplication by A01.
> Decreasing that cost would be nice (I attached the output of -log_summary
> for reference).
> I think I need to look for the objects that are not Destroyed too.
>

We will look, but this is a notoriously hard thing to speed up. You might
try the RAP code instead.

Finally I now would like to split the Schur complement into two
> submatrices. I have an IS that tracks location of these sub-matrices in the
> global system:
>
>        [ A00  A01  A02 ]  --> IS(0)
> A = [ A10  A11  A12 ]  --> IS(1)
>        [ A20  A21  A22 ]  --> IS(2)
>
> How can I use IS(1) and IS(2) to track:
>
> S =   [ A11  A12 ]  _  [ A10] * [A00]^-1 * [ A01 A02 ]  = [ S11  S12 ]
> --> IS(1)'
>          [ A21  A22 ]     [ A20]
> = [ S21  S22 ]  --> IS(2)'
>
> or is there a simple way to compute IS(1)' and IS(2)' based on IS(1) and
> IS(2)?
>

Aren't they identical?

  Thanks,

     Matt


> Thanks!
>
> Best,
> Luc
>
> On 03/26/2015 04:12 PM, Matthew Knepley wrote:
>
>  On Thu, Mar 26, 2015 at 3:07 PM, Luc Berger-Vergiat <lb2653 at columbia.edu>
> wrote:
>
>> Hi all,
>> I want to multiply two matrices together, one is MATAIJ and the second is
>> MATBAIJ, is there a way to leverage the properties of the blocked matrix in
>> the BAIJ format or should I just assemble the BAIJ matrix as AIJ?
>
>
>  I am afraid you are currently stuck with the latter.
>
>    Thanks,
>
>      Matt
>
>
>>
>> --
>> Best,
>> Luc
>>
>>
>>
>
>
>  --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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